1. Field of the Invention
The present invention relates to three winding transformers, and particularly to a large-capacity three winding transformer using two parallel-connected tap changers which are connected to a middle voltage winding, for tap change-over upon loading.
2. Description of the Prior Art
The large-capacity three winding transformer for tap change-over upon loading at a middle voltage generally includes, as shown in, for example, FIG. 1 or 3, a magnetic core 11 wound thereon with the following windings, a low voltage winding 12, a middle voltage winding 13, a high voltage winding 14, and two tapped windings 15a and 15b or one tapped winding 15 which are each connected in series with the middle voltage winding 13, and of which the taps are changed over by two load tap changers 16a and 16b or one load tap changer 16, respectively.
FIG. 1 shows a three winding transformer having the magnetic core 11 on which are wound the low voltage winding 12, the middle voltage winding 13 and the high voltage winding 14 in order. The two tapped windings 15a and 15b are disposed on the outside of and are coaxial with the high voltage winding 14 and the two tapped windings 15a and 15b are separated a predetermined distance from each other. In FIG. 1, L.sub.1 and L.sub.2 represent low voltage terminals of the low voltage winding 12, M.sub.1 and M.sub.0 a line terminal and a neutral terminal of the middle voltage winding 13, respectively and H.sub.1 and H.sub.0 a line terminal and a neutral terminal of the high voltage terminal 14, respectively.
If the three winding transformer as shown in FIG. 1 is required to be of large capacity and to have a large current capacity of the middle voltage winding 13, the middle voltage winding 13 is formed by two windings 13a and 13b as shown in FIG. 2. The two windings 13a and 13b are connected in series with two load tap changers 16a and 16b, respectively, and the two series circuits are parallel-connected to form the whole middle voltage winding. These two parallel-connected load tap changers 16a and 16b have polarity change-over switches 20a and 20b, tap windings 15a and 15b, tap selectors 18a and 18b, and change-over switches 17a and 17b, which are connected in series with the middle voltage windings 13a and 13b, respectively.
If the taps of each tap winding 15a, 15b are selected in such a parallel circuit, the change-over switches 17a and 17b of the load tap changers 16a and 16b may become different in switching time to cause a potential difference equivalent to one-tap distance of the tapped windings 15a and 15b, and this potential difference may be applied in the parallel circuit consisting of the series circuit of the middle voltage winding 13a, the polarity change-over switch 20a, the tapped winding 15a, the tap selector 18a and the change-over switch 17a and the series circuit of the middle voltage winding 13b, the polarity change-over switch 20b, the tapped winding 15b, the tap selector 18b and the change-over switch 17b. If this potential is taken as e.sub.1, a circulating current I.sub.c depending on the e.sub.1 and the impedance Z of the parallel circuit is flowed in the parallel circuit. In the two parallel-connected middle voltage windings as shown in FIG. 2, an inductance L of the middle voltage windings for the circulating current I.sub.c is expressed by EQU L=L.sub.13a +L.sub.13b +2M.sub.13ab,
where L.sub.13a and L.sub.13b are self inductances of the middle voltage windings 13a and 13b, respectively and M.sub.13ab is a mutual inductance between the middle voltage windings 13a and 13b. When the circulating current I.sub.c is flowed through the windings 13a and 13b, the magnetic flux induced by the winding 13a can be opposite in direction to that induced by the winding 13b, so that the mutual inductance M.sub.13ab can be negative. Moreover, the self inductances L.sub.13a and L.sub.13b and the mutual inductance L.sub.13ab can be expressed by EQU L.sub.13a =.mu.SN.sub.13a.sup.2 /l (1) EQU L.sub.13b =.mu.SN.sub.13b.sup.2 /l (2) EQU M.sub.13ab =K.sqroot.L.sub.13a .multidot.L.sub.13b ( 3)
where .mu. is the permeability of the magnetic circuit, S the cross-sectional area of the magnetic circuit, N.sub.13a the number of turns of the winding 13a and N.sub.13b the number of turns of the winding 13b, l the length of the magnetic circuit, and K the coupling coefficient.
Since the middle voltage windings 13a and 13b can be closely coupled to each other, that is, the coupling coefficient K is equivalent to one, the inductance L becomes zero. Therefore, the impedance of the middle voltage windings 13a and 13b for the circulating current is only a winding resistance R, which is about 0.1 to 0.3 ohm in a large-capacity transformer. Consequently, the total series impedance of the middle windings 13a and 13b is about 0.1 to 0.3 ohm which is the winding resistance R.
In practice, however, the tapped windings 15a and 15b are respectively connected in series with the middle windings 13a and 13b and also coaxially disposed at upper and lower positions separated by a predetermined distance. In addition, the tapped windings 15a and 15b are so wound that by the circulating current I.sub.c the magnetic flux induced in the tapped winding 15a is opposite in direction to that in the tapped winding 15b. Thus, the tapped windings 15a and 15b have approximately zero coupling coefficient and hence the inductance thereof is not zero.
In a three winding transformer of, for example, ##EQU1## (tap voltage, (220.+-.33)/.sqroot.3) class, the total series impedance of the middle windings and tapped windings for the circulating current flowing therethrough is about 5 ohms. That is, the impedance Z for the circulating current I.sub.c in the parallel circuit as shown in FIG. 2 is about 5 ohms, and in this case the potential difference e.sub.1 between the taps is about 2000 to 3000 volts. Thus, the circulating current I.sub.c amounts to about several hundred amperes. The circulating current I.sub.c is superimposed upon a load current to exceed the cutoff current (in the above example, about 2500 A) of the tap changer 16a, 16b, so that the tap changers do not operate to cut off. It is also uneconomical to install a large-capacity tap changer capable of accepting this very large amount of circulating current I.sub.c.
FIG. 3 shows a large-capacity three winding transformer with a middle voltage winding 13 of a large-current capacity. In this three winding transformer, the cutoff current value of the change-over switch in the load tap changer may sometimes exceed an allowable value. In this case, the tap winding 15 is formed of two coaxially disposed parallel windings 15a and 15b as shown in FIG. 4. These two parallel windings 15a and 15b are connected with the polarity change-over switches 20a and 20b, the tap selectors 18a and 18b and the change-over switches 17a and 17b, thus constituting two parallel load tap changers 16a and 16b, respectively.
Since the tapped windings 15a and 15b are coaxially disposed, when a load current flows, the tapped winding 15a is interlinked with a magnetic flux .PHI..sub.a, and the tapped winding 15b with a magnetic flux .PHI..sub.b. If, in this case, the amount of interlinkage flux in the tapped winding 15a is compared with that in the tapped winding 15b by using the average diameters of both the windings, the relation of .PHI..sub.b .apprxeq.9.PHI..sub.a results. Thus, the induced voltages by the respective interlinkage flux are not cancelled out. If the number of turns of the tapped winding 15a, 15b is taken as N, and the frequency as f, then the induced voltages e.sub.a and e.sub.b in the tapped windings 15a and 15b and the difference voltage e therebetween are given as follows: EQU e.sub.a =4.44.pi.fN.PHI..sub.a ( 4) EQU e.sub.b =4.44.pi.fN.PHI..sub.b ( 5) EQU e=e.sub.b -e.sub.a =4.44.pi.fN8.PHI..sub.a ( 6)
This induced voltage e is generated in the parallel circuit to cause the circulating current I.sub.c to be flowed in the parallel circuit against the impedance Z thereof which determines the value of the current I.sub.c.
The inductance L for the circulating current I.sub.c can be expressed by EQU L=L.sub.15a +L.sub.15b +2M.sub.15ab ( 7)
where L.sub.15a and L.sub.15b represent the self inductances of the tapped windings 15a and 15b, respectively, and M.sub.15ab the mutual inductance between the tapped windings 15a and 15b. The self inductances L.sub.15a and L.sub.15b and the mutual inductance M.sub.15ab are expressed by EQU L.sub.15a =.mu.SN.sub.15a.sup.2 /l (8) EQU L.sub.15b =.mu.SN.sub.15b.sup.2 /l (9) EQU M.sub.15ab =K.sqroot.L.sub.15a.sup.2 .multidot.L.sub.15b.sup.2 ( 10)
where N.sub.15a and N.sub.15b are the numbers of turns of the tapped windings 15a and 15b, respectively.
Also in this case, the mutual inductance M.sub.15ab is negative similar to that in the above description, and thus the impedance Z is only the winding resistance. The resultant current of the circulating current I.sub.c and the winding load current I.sub.e may be about 130 to 150% of the winding load current depending on the selected tap. In the transformer of ##EQU2## (tap voltage, (220.+-.33)/.sqroot.3) class, the resultant current of the circulating current I.sub.c and the winding load current I.sub.e is about 140% of the winding load current. Thus, in the three winding transformer of the construction shown in FIG. 4, the same trouble as that in FIG. 1 is caused by the untimely operation of the change-over switches 17a and 17b.